1. To determine whether two lines are parallel, perpendicular, or neither, we need to compare their slopes. The given equation is written in slope-intercept form, which is y = mx + b, where m represents the slope of the line.
In the given equation y = -3/4x - 2, the slope is -3/4.
If two lines are perpendicular, their slopes are negative reciprocals of each other. The negative reciprocal of -3/4 is 4/3.
Therefore, since the slope of the given equation is -3/4 and the negative reciprocal of that is 4/3, the lines are perpendicular.
The correct answer is B. Perpendicular.
2. To find the equation of a line that is perpendicular to the given line and passes through the given point, we need to determine the slope of the given line and then find its negative reciprocal.
The given equation is y - 3 = -1/5 (x + 2). To find the slope of this line, we can rewrite the equation in slope-intercept form.
y - 3 = -1/5 (x + 2)
y - 3 = -1/5x - 2/5
y = -1/5x - 2/5 + 3
y = -1/5x - 2/5 + 15/5
y = -1/5x + 13/5
The slope of the given line is -1/5.
To find the slope of the line perpendicular to this, we take the negative reciprocal of -1/5. The negative reciprocal of -1/5 is 5/1 or simply 5.
Now we have the slope of the perpendicular line, which is 5, and the point through which it passes, which is (-2, 7). We can use the point-slope form of the equation, y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope.
Plugging in the values, we get:
y - 7 = 5(x + 2)
Simplifying this, we have:
y - 7 = 5x + 10
y = 5x + 17
Therefore, the equation of the line that is perpendicular to the given line and passes through the given point (-2, 7) is y = 5x + 17.
The correct answer is B. y = 5x + 17.